Control of Kirchhoff vortices by a resonant strain

Abstract

It is shown that placing a Kirchhoff vortex in a weak resonant strain having uniform, but oscillating strain rate with chirped oscillation frequency, allows adiabatic control of the axis ratio $\ensuremath{\rho}=a/b$ and rotation phase of the vortex. The phenomenon has a threshold on the amplitude of oscillations of the strain rate and is due to the persisting nonlinear phase locking (autoresonance) between the elliptic vortex and the adiabatically varying straining flow.